# What are the points of inflection, if any, of #f(x)=-3x^3+270x^2-3600x+18000 #?

At

Given -

We must set the send derivative to zero in order to determine the point of inflection.

Then -

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To find the points of inflection, we first need to find the second derivative of the function and then solve for the values of x where the second derivative equals zero or is undefined.

The first derivative of ( f(x) ) is: ( f'(x) = -9x^2 + 540x - 3600 )

The second derivative of ( f(x) ) is: ( f''(x) = -18x + 540 )

Setting ( f''(x) ) equal to zero and solving for x: ( -18x + 540 = 0 ) ( x = 30 )

So, the point of inflection is ( (30, f(30)) ).

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